Question

A wave is travelling in the negative direction of x-axis then its equation is?

Answer 1

Answer:

Y = A Cos (ω t - k x + Ф)   is the equation of a wave that is travelling in positive x direction with a velocity  v.

             ω = frequency and is positive.

                 k = wave number and is positive.

             Ф = initial phase value at t = 0 at origin x = 0.

So  at t = 0, at x = X1,       y = A Cos (Ф -  k X1)

At t = Δt , at X1 +Δx,  let  y be the same, or the phase of the wave be the same:

  hence,   y = A Cos (ω Δt - k X1 - k Δx + Ф) =  A Cos (Ф - k X1)

                 so  ω Δt =  k Δx

                    Δx / Δt = ω / k  = velocity of the wave in the + ve x direction.

  As the point that has the same constant phase value, travels in +ve x direction with the above speed.

Then for getting the velocity of the wave in the negative x direction, replace x by -x.

     y = A Cos (ω t + k x +Ф)

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